Error analysis of linearized semi-implicit galerkin finite element methods for nonlinear parabolic equations

Buyang Li, Weiwei Sun

Research output: Journal article publicationJournal articleAcademic researchpeer-review

105 Citations (Scopus)


This paper is concerned with the time-step condition of commonly-used linearized semi-implicit schemes for nonlinear parabolic PDEs with Galerkin finite element approximations. In particular, we study the time-dependent nonlinear Joule heating equations. We present optimal error estimates of the semi-implicit Euler scheme in both the L2 norm and the H1 norm without any time-step restriction. Theoretical analysis is based on a new splitting of error function and precise analysis of a corresponding time-discrete system. The method used in this paper is appli- cable for more general nonlinear parabolic systems and many other linearized (semi)-implicit time discretizations for which previous works often require certain restriction on the time-step size τ.
Original languageEnglish
Pages (from-to)622-633
Number of pages12
JournalInternational Journal of Numerical Analysis and Modeling
Issue number3
Publication statusPublished - 14 Jun 2013
Externally publishedYes


  • Galerkin method
  • Linearized semi- implicit scheme
  • Nonlinear parabolic system
  • Unconditionally optimal error estimate

ASJC Scopus subject areas

  • Numerical Analysis

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